How to pass Comparator to user define Templeted class? - c++11

Question

I want to create a generalized heap data structure, and facing an issue with passing template comparator.
template<typename T, typename C = less<T> > class Heap{
vector<T> *heap;
public:
Heap(vector<T> *arr){
heap = new vector<T> (arr->begin(), arr->end());
build_heap();
}
void build_heap(){
size_t n = heap->size();
for (size_t i=(n-1)/2; i>=0; i--){
shiftDown(i);
}
}
void shiftDown(size_t i){ /// heap logic
while(i < heap->size()){
size_t child = 2*i+1;
// int min_ind = 2*i+1;
if(child >= heap->size())
return;
if(child+1 < heap->size()){
if( C(heap->at(child+1),heap->at(child)) ){ // <----- using C as comparator
child++;
}
}
if( C(heap->at(child), heap->at(i)) ){ // <----- using C as comparator
swap(heap->at(child), heap->at(i));
i = child;
}
else
break;
}
}
};
int main(){
vector<int> v={8,7,6,5,4,3,2,1};
Heap<int, less<int> > heap(&v);
}
error
heap.cpp: In instantiation of ‘void Heap<T, C>::shiftDown(size_t) [with T = int; C = std::less<int>; size_t = long unsigned int]’:
heap.cpp:15:4: required from ‘void Heap<T, C>::build_heap() [with T = int; C = std::less<int>]’
heap.cpp:10:3: required from ‘Heap<T, C>::Heap(std::vector<_Tp>*) [with T = int; C = std::less<int>]’
heap.cpp:49:34: required from here
heap.cpp:32:9: error: no matching function for call to ‘std::less<int>::less(__gnu_cxx::__alloc_traits<std::allocator<int>, int>::value_type&, __gnu_cxx::__alloc_traits<std::allocator<int>, int>::value_type&)’
32 | if( C(heap->at(child+1),heap->at(child)) ){
| ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
...
detailed error
i'm following same syntex of declaration as stl c++ do, still i'm getting error. please help me out.
template<typename T, typename C = less<T> > class Heap;
any help or pointer to help is appreciated. thank you.

Answer 1

template<class T>
class Comparator{
bool operator()(const T &a, const T &b){
...
// returns logic
}
}
template<class T, class Comp >
class AnyClass{
public:
...
void function(){
// code ...
Comp<T>()(obj1, obj2);
}
...
}
calling sytex :
...
AnyClass *obj = new AnyClass<Type , Comparator>();
obj.function()
...
passing Comparator to templated class and when we need to compare objects
we create a functional object and call operator() with args to compare.
In question, that object is less<int>.
Comp<T>()(obj1, obj2);